OFFSET
2,2
COMMENTS
Number of ascending runs of length at least two in all permutations of [n]. Example: a(3)=5 because we have (123), (13)2, 3(12), 2(13), (23)1 and 321, where the ascending runs of length at least 2 are shown between parentheses. - Emeric Deutsch and Ira M. Gessel, Sep 07 2004
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
J. Francon, Histoires de fichiers, RAIRO Informatique Théorique et Applications, 12 (1978), 49-62.
J. Francon, Histoires de fichiers, RAIRO Informatique Théorique et Applications, 12 (1978), 49-62. (Annotated scanned copy)
FORMULA
a(n) = (2n-1)/6 * n!.
E.g.f.: x^2*(3-x)/(6*(1-x)^2). - Emeric Deutsch and Ira M. Gessel, Sep 07 2004
MATHEMATICA
Table[(2n-1)/6*n!, {n, 2, 30}] (* Harvey P. Dale, Jan 06 2014 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Harvey P. Dale, Jan 06 2014
STATUS
approved